neural inverse space mapping em-optimization...neural inverse space mapping em-optimization j.w....

Neural Inverse Space Mapping EM-Optimization

J.W. Bandler, M.A. Ismail, J.E. Rayas-Sánchez and Q.J. Zhang

Simulation Optimization Systems Research Laboratory McMaster University

Bandler Corporation, [email protected]

presented at

2001 IEEE MTT-S International Microwave Symposium, Phoenix, AZ, May 23, 2001

Neural Inverse Space Mapping EM-Optimization (NISM)

outline

ANN approaches for microwave design

NISM optimization

statistical parameter extraction

inverse neuromapping

the NISM step vs. the quasi-Newton step

examples

conclusions

Simulation Optimization Systems Research LaboratoryMcMaster University

Conventional ANN-Based Optimization of Microwave Circuits(Zaabab, Zhang and Nakhla, 1995, Gupta et al., 1997, Burrascano and Mongiardo, 1998)

step 1


ANN

finemodel

ωRfxf

≈ Rf

w

step 2

ANN ≈ R*xf

ω

many fine model simulations are usually needed

solutions predicted outside the training region are unreliable

ANN-Based Microwave Optimization Exploiting Available Knowledge

EM-ANN approach(Gupta et al., 1999)


neural space mapping approach(Bandler et al., 2000)

neuro-mapping

finemodel

ωRfxf

Rc ≈ Rf

w

coarsemodel

xc

ωc

NSM optimization requires 2n+1 upfront fine simulations

coarsemodel

ANN

finemodel

ω Rf

Rc

∆R

≈ ∆R

xf

w

Objectives

develop an aggressive ANN-based space mapping optimization

avoid multipoint parameter extraction and frequency mappings


Neural Inverse Space Mapping Optimization


Calculate the fine responsesRf s(xf

(i))

PARAMETER EXTRACTION:Find xc

(i) such that

Rcs(xc(i)) ≈ Rf s(xf

(i))

xf(i) = xc

* INVERSENEUROMAPPING:

Find the simplest neuralnetwork N such that

xf (l) ≈ N (xc

(l))

l = 1,..., i

xf (i+1) = N(xc

*)i = i + 1 xf(i) ≈ xf

(i+1)no

yes

End

COARSE OPTIMIZATION: find theoptimal coarse model solution xc

* thatgenerates the desired response

Start

i = 1

Statistical Parameter Extraction


(1)

)(minarg)(cPE

ic U

cxxx =

22)()( ccPEU xex =

)()()( )(ccs

iffsc xRxRxe −=

begin

solve (1) using as starting point

while

calculate using (2) and (3)

solve (1) using as starting point

end

xx ∆+*c

PEi

c ε>∞

)( )(xe

x∆

*cx

(2)

∞∇

=)( *max

cPE

PE

U xδ∆

(3)

)12(max −= kk randx ∆∆

nk K1=

Inverse Neuromapping


(4)

)(minarg* www NU=

2

2][)( TT

lNU LL ew =

),( )()( wxNxe lc

lfl −=

il ,,1K=

begin

solve (4) using a 2LP

h = n

while UN (w*) > εL

solve (4) using a 3LP

h = h + 1

endxc xf

N

ANN (2LP or 3LP)

w

Nature of the NISM Step

xf(i+1) = N(xc

*)

evaluates the current ANN at the optimal coarse solution

is equivalent to a quasi-Newton step

departs from a quasi-Newton step as the nonlinearity needed in the inverse mapping increases

does not use classical updating formulas to approximate the Jacobianinverse


Termination Condition for NISM Optimization


niifendend

if

if 3)(

2

)(

2

)()1( =∨+≤−+ xxx εε

HTS Quarter-Wave Parallel Coupled-Line Microstrip Filter(Westinghouse, 1993)


εr

L2

L1L0

L3

L2

L1

L0

S2 S1

S1 S2

S3

HW

we take L0 = 50 mil, H = 20 mil, W = 7 mil, εr = 23.425, loss tangent = 3×10−5; the metalization is considered lossless

the design parameters are

xf = [L1 L2 L3 S1 S2 S3] T

specifications

|S21| ≥ 0.95 for 4.008 GHz ≤ ω ≤ 4.058 GHz|S21| ≤ 0.05 for ω ≤ 3.967 GHz and ω ≥ 4.099 GHz

HTS Microstrip Filter: Fine and Coarse Models

fine model:

Sonnet’s em with high resolution grid


1

2

coarse model:

OSA90/hope built-in models of open circuits, microstrip lines and coupled microstrip lines

NISM Optimization of the HTS Filter

responses using em (o) and OSA90/hope (−)

at the starting point


3.95 4 4.05 4.1 4.150

0.2

0.4

0.6

0.8

1

frequency (GHz)

|S21

|

NISM Optimization of the HTS Filter (continued)

responses using OSA90/hope (−) at xc* and em (o) at the NISM solution

(after 3 NISM iterations)


3.95 4 4.05 4.1 4.150

0.2

0.4

0.6

0.8

1

frequency (GHz)

|S21

|

NISM vs. NSM Optimization

HTS filter optimal responses in the passband

after NISM (3 fine simulations)


3.98 4 4.02 4.04 4.06 4.080.8

0.85

0.9

0.95

1

frequency (GHz)

|S21

|

after NSM (14 fine simulations)(Bandler et al., 2000)

3.98 4 4.02 4.04 4.06 4.080.8

0.85

0.9

0.95

1

frequency (GHz)

|S21

|

NISM vs. Trust Region Aggressive Space Mapping (TRASM) Exploiting Surrogates

fine model minimax objective function

after NISM (3 fine simulations)


after TRASM Exploiting Surrogates (8 fine simulations) (Bakr et al., 2000)

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1.0

iteration

fine

mod

el m

inim

ax o

bjec

tive

func

tion

1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

iteration

fine

mod

el m

inim

ax o

bjec

tive

func

tion

Conclusions

we propose Neural Inverse Space Mapping (NISM) optimization

up-front EM simulations, multipoint parameter extraction or frequency mapping are not required

a statistical procedure overcomes poor local minima during parameter extraction

an ANN approximates the inverse of the mapping

the next iterate is obtained from evaluating the ANN at the optimal coarse solution

this is a quasi-Newton step

NISM optimization exhibits superior performance to NSM optimization and Trust Region Aggressive Space Mapping Exploiting Surrogates


neural inverse space mapping em-optimization...neural inverse space mapping em-optimization j.w....

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